Sunday, December 15, 2013

Toward Competent Genetic Algorithms: Linkage Learning

We
endorse the term Competent Genetic
Algorithms to those GAs that solve hard problems quickly, accurately and
reliably [1]. We already know that GAs process building blocks (BB): low
order---few specific bits---and low length---small distance between specific
bits---schema with above average fitness. However, crossover may disturb these
BB. Ideally, crossover should identify the fundamental BB of the problem at
hand and mix them well, but in the real world this phenomenon scarcely happens.
In order to tackle this issue a radical approach is required: remove the
classic selecto-recombinative operators out of the GA loop and develop
strategies that automatically identify BBs ensuring that these are not
disrupted. Researchers call this strategy as Linkage Learning [2].

Estimation
of Distribution Algorithms (EDAs) use probabilistic models that perform the
task. They learn a probabilistic model and then build new solutions by sampling
candidates from the model.

One
of the simplest forms of EDA is the so-called compact genetic algorithm (cGA,
[2]). CGA uses a probability vector to represent populations of strings.
Furthermore, population is completely replaced by this probability vector---i.e.,
no explicit population is stored in memory, hence its name. At each iteration
cGA generates two solutions out of the probability vector. Then it evaluates
these two solutions and finally it updates the probability vector according to
the fitness computation.

I
coded a simple cGA in R solving the trap-n function: a simple boolean function
that is deceptive---i.e., it is misleading toward local optima [1].

The
situation is the following: for n = 5, the learner has to reach the chromosome
11111, but the fitness computation misleads the search towards 00000 (a local
optima!). Figure 1 depicts this situation in the trap-5 function. This problem
is hard for a traditional GA (specially for the simple GA), but cGA solves it quickly
and accurately.

Edit: notice that Figure 1 depicted a distinct trap-5 function---in the picture version of the function I forgot to count 0 as a valid solution. Also notice that the fitness function leads the system toward 00000 and not 00001.